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A characterization of order statistic point processes that are mixed Poisson processes and mixed sample processes simultaneously

Published online by Cambridge University Press:  14 July 2016

A. Deffner  and
E. Haeusler
A. Deffner
Affiliation:
University of Munich
E. Haeusler*
Affiliation:
University of Munich
*
∗Postal address: Mathematical Institute, University of Munich, Theresienstrasse 39, D-8000 Munich 2, West Germany.
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Abstract

The results of Nawrotzki (1962), Feigin (1979) and Puri (1982) show that the class of all point processes (on the real line) with the order statistic property consists of all mixed Poisson processes up to a time-scale transformation, and of all mixed sample processes. The present note characterizes those order statistic point processes that are mixed Poisson processes and mixed sample processes simultaneously.

Keywords

ORDER STATISTIC PROPERTYSTIELTJES MOMENT PROBLEM
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 2 , June 1985 , pp. 314 - 323
Copyright
Copyright © Applied Probability Trust 1985 

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References

Billingsley, P. (1979) Probability and Measure. Wiley, New York.Google Scholar
Crump, K. S. (1975) On point processes having an order statistic structure. Sankhya A 37, 396–404.Google Scholar
Feigin, P. D. (1979) On the characterization of point processes with the order statistic property. J. Appl. Prob. 16, 297–304.Google Scholar
Nawrotzki, K. (1962) Ein Grenzwertsatz für homogene zufällige Punktfolgen. Math. Nachr. 24, 201–217.Google Scholar
Puri, P. S. (1982) On the characterization of point processes with the order statistic property without the moment condition. J. Appl. Prob. 19, 39–51.Google Scholar